1. Field of the Invention
The present invention relates to a method of controlling the position of a rotary shaft in a magnetic bearing.
2. Description of the Prior Art
Because the magnetic bearing carries a rotary member in the air by the magnetic force without requiring physical contact, the magnetic bearing is characterized in that no problem is encountered in lubrication, it can be used in a specific environment, for example under vacuum, the bearing loss is small, the noise is small, and little maintenance is required. By taking advantage of these features, the magnetic bearing is frequently used in a high-speed processing machine or a vacuum pump.
FIG. 1 depicts a conventional magnetic bearing having a shell 11 securely mounted on, for example, a processing machine (not shown). Inside the shell 11 are mounted a rotary shaft 20, a motor stator 12, a plurality of electric magnets 13a1-13a4 (only 13a1 and 13a3 are shown), 13b1-13b4 (only 13b1 and 13b3 are shown), and 14, and a plurality of displacement detection sensors 15a, 15b, and 16 for detecting the position of the rotary shaft 20. Two electromagnetic attraction members 18a and 18b are securely mounted on the rotary shaft 20 so as to confront the electric magnets 13a1-13a4 and the electric magnets 13b1-13b4, respectively. Each of the electromagnetic attraction members 18a and 18b is made of silicon steel plates laminated one upon another. An electromagnetic attraction member 19 made of steel is securely mounted on or integrally formed with the rotary shaft 20 so that the electric magnets 14 may confront a peripheral portion of the attraction member 19. The position of the rotary shaft 20 is maintained by the attraction members 18a and 18b and the electric magnets 13a1-13a4 and 13b1-13b4 in the radial direction, and by the attraction member 19 and the electric magnets 14 in the axial direction.
FIG. 2 depicts a conventional control system for controlling the radial position of the rotary shaft 20. The control system performs a feedback control to change the magnetic attraction of the electric magnets 13a1-13a4, 13b1-13b4, and 14, thereby maintaining the rotary shaft 20 substantially at the same position in the air. More specifically, the system controls the radial position of the rotary shaft 20 so that the spacing D, detected by the sensors 15a and 15b, between the rotary shaft 20 and the sensors 15a and 15b may be in agreement with the present value D2. As shown in FIG. 2, each set of the electric magnets 13a1-13a4 and the electric magnets 13b1-13b4 is independently controlled by a PID regulator 21 via respective control current gains 22. In FIG. 2, the electric magnets 14 for controlling the axial position of the rotary shaft 20 are omitted for brevity's sake.
In the above-described independent control of the electric magnets, however, a mutual interference occurs in magnetic attraction and interrupts the steady support of the rotary shaft 20 in the air.
The mutual interference in magnetic attraction is discussed hereinafter with reference to FIG. 3, wherein a coordinate system is defined with the position of the center of gravity G of the rotary shaft as the origin. The gravity is neglected for brevity's sake. Equations of motion of the rotary shaft are as follows. EQU mx=F.sub.1 -F.sub.3 +F.sub.5 -F.sub.7 (Equation of translation in X-direction) EQU my=F.sub.2 -F.sub.4 +F.sub.6 -F.sub.8 (Equation of translation in Y-direction) EQU J.sub.r .theta..sub.x +J.sub.a .omega..theta..sub.y =-(F.sub.2 -F.sub.4)l.sub.f +(F.sub.6 -F.sub.8)l.sub.r (Equation of rotation in .theta..sub.x -direction) EQU J.sub.r .theta..sub.x +J.sub.a .omega..theta..sub.y =(F.sub.1 -F.sub.3)l.sub.f +(F.sub.5 -F.sub.7)l.sub.r (Equation of rotation in .theta..sub.y -direction) (1)
where
m: mass of rotary shaft, PA1 F.sub.n : attraction of each electric magnet (N=1-8), PA1 J.sub.r : moment of inertia of rotary shaft about Z-axis, PA1 J.sub.a : moment of inertia of rotary shaft about X-axis or PA1 Y-axis, PA1 .omega.: angular velocity of rotary shaft, PA1 l.sub.f : distance between the center of gravity and front electric magnets, and PA1 l.sub.r : distance between the center of gravity and rear electric magnets. PA1 D.sub.n : spacing between electric magnets and rotary shaft, D.sub.n =D.sub.n +d and PA1 K.sub.n : constant determined from the property of each electric magnet. PA1 A.sub.1 =2(K.sub.Df +K.sub.Dr) PA1 A.sub.2 =2(K.sub.Df l.sub.f -K.sub.Dr l.sub.r) PA1 B.sub.x =2(K.sub.If i.sub.fx +K.sub.If i.sub.rx) PA1 B.sub.y =2(K.sub.If i.sub.fy +K.sub.If i.sub.ry) EQU J.sub.r .theta..sub.x +J.sub.a .omega..theta..sub.y -A.sub.3 .theta..sub.x +A.sub.4 y=C.sub.x (Equation of rotation in .theta..sub.x -direction) EQU J.sub.r .theta..sub.y +J.sub.a .omega..theta..sub.x -A.sub.3 .theta..sub.y +A.sub.4 x=C.sub.y (Equation of rotation in .theta..sub.y -direction)(5) PA1 A.sub.3 =2(K.sub.Df l.sub.f.sup.2 +K.sub.Dr l.sub.r.sup.2) PA1 A.sub.4 =2(K.sub.Df l.sub.f -K.sub.Dr l.sub.r) PA1 C.sub.x =-2(K.sub.If l.sub.f i.sub.fy -K.sub.Ir l.sub.r i.sub.ry) PA1 C.sub.y =2(K.sub.If l.sub.f i.sub.fx -K.sub.Ir l.sub.r i.sub.rx)
It is to be noted here that, in FIG. 3, the left-hand side is the front side of the magnetic bearing.
The attraction F.sub.n of each electric magnet is given by: ##EQU1## where I.sub.n : exciting current, I.sub.n =I.sub.n +i
Because the amount of change i of I and the amount of change d of D are very small relative to I and D in the equilibrium condition, terms of i/I and d/D having an exponent of 2 or greater are neglected. In this case, the attraction F.sub.n of each electric magnet is expanded as follows: ##EQU2##
Let the property K and the spacing D associated with the front four electric magnets be the same and let those associated with the rear four electric magnets be the same. When the variables I.sub.n, D.sub.n, K.sub.n, K.sub.In, and K.sub.Dn associated with each electric magnet is represented by a variable .phi..sub.n, .phi..sub.f =.phi..sub.1.about. .phi..sub.4 and .phi..sub.r =.phi..sub.5.about. .phi..sub.8 hold. It is to be noted that subscripts f and r indicate the front side and the rear side, respectively. When a control current i flowing in one electric magnet is rendered to be the same in magnitude as that flowing in another electric magnet opposed thereto with plus and minus reversed, the relationships of i.sub.4 =-i.sub.2 and i.sub.3 =-i.sub.1 hold, where i.sub.1, i.sub.2, i.sub.3, and i.sub.4 are the control currents flowing in the electric magnets 13a1, 13a2, 13a3, and 13a4, respectively. In this case, the equations of motion of the rotary shaft can be simplified as follows. EQU mx-A.sub.i x-A.sub.2 .theta..sub.y =B.sub.x (Equation of translation in X-direction) EQU my-A.sub.i y+A.sub.2 .theta..sub.x =B.sub.y (Equation of translation in Y-direction) (4)
The equation of translation in the X-direction includes a rotational component .theta.y at the third term of the left side thereof, whereas the equation of translation in the Y-direction includes a rotational component .theta.x at the third term of the left side thereof. The equation of rotary motion in the .theta.x-direction includes a rotational component .theta.y (gyro effect) and a translation component y at the second and fourth terms of the left side thereof, respectively. When the rotary shaft is long and slender, the moment of inertia J.sub.a is small, and when the angular velocity .omega. is small, the influence of the gyro effect can be neglected. Accordingly, the interference is caused only by the translation component y. Similarly, the equation of rotary motion in the .theta.y-direction includes a translation component x in the left side thereof. Because of this, the mutual interference is caused among all of the equations of translation and those of rotary motion.
To solve this problem, another control system has hitherto been proposed wherein four front electric magnets and four rear electric magnets are controlled as one system by separating the attitude of the rotary shaft into the translation components and the rotational components. In this system, the control current i indicated in the right sides of Equations (4) and (5) is constituted by the sum of a control current i.sub.H of the translation and a control current i.sub.K of the rotary motion. When the current value i.sub.n in the right side of Equation (4) corresponding to the controlled variable is changed so that the displacement of the center of gravity may become 0 to satisfy the equation of translation, the values of C in the right sides of Equation (5) also change. As a result, the angle of displacement about the center of gravity changes. Likewise, when the current value i.sub.n in the right side of Equation (5) corresponding to the controlled variable is changed so that the angle of displacement about the center of gravity may become 0 to satisfy the equation of rotary motion, the values of B in the right sides of Equation (4) also change. As a result, the position in the direction of translation changes, and a problem of mutual interference is encountered, which differs from the aforementioned mutual interference caused by the property K.sub.D of each electric magnet and the biasing current I. Although it is generally known that the use of a technique on the basis of the modern control theory is suited in controlling such a multiinput-multioutput system with accuracy, this kind of technique includes a problem in that the determination of parameters or the calculation are too complicated to be practical.